Question

Solve by using the Quadratic Formula: $x(x+2)-5=0$

Short answer

The solution of the quadratic equation is$x=-1\pm \sqrt{6}$

Step-by-step solution

Step `1: Given information

We are given a quadratic equation$x(x+2)-5=0$

Distribute and write the equation in standard form

On distributing we get

$x^2+2x-5=0$

Identify the values of a,b,cand write the quadratic formula

On comparing with standard equation we get $a=1,b=2,c=-5$

The quadratic formula can be given as

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute the values in the quadratic formula and simplify

We substitute the values in the formula we get,

$$\begin{gathered} x=\frac{-2\pm \sqrt{4-4(-5)}}{2} \\ x=\frac{-2\pm \sqrt{4+20}}{2} \\ x=\frac{-2\pm \sqrt{24}}{2} \\ x=\frac{-2\pm 2\sqrt{6}}{2} \end{gathered}$$

Find the common factor and remove it

We find the common factor

$$\begin{gathered} x=\frac{2(-1\pm \sqrt{6})}{2} \\ x=-1\pm \sqrt{6} \end{gathered}$$

Conclusion

The solution of the above equation is$x=-1\pm \sqrt{6}$